Thumbtack·Data Scientist·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Thumbtack data scientist interview with a pretty involved stats question about regional response rate analysis. One question, but it had a lot of moving parts and I felt like I was being tested on five different things at once.

Questions Asked (1)

Given job-level data with fields like job category, region, invitations sent, provider responses, and date, how would you determine whether response rates differ by region after controlling for job category mix and time? Walk through your model specification, how you'd handle standard errors, multiple comparisons across many regions, Simpson's paradox detection, and how you'd communicate effect sizes beyond just p-values.

A/B Testing & ExperimentationProduct Analytics & MetricsData Modeling

Author's notes

This was a lot to hold in your head at once.

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AI HintsAI Generated

Suggested Approach

Start by framing the problem as estimating region effects on response rate while adjusting for job category mix and temporal trends. Propose a regression model with region fixed effects, job category fixed effects, and time controls (e.g., week fixed effects), then discuss robust standard errors, multiple comparison corrections, and effect size communication. Emphasize checking for Simpson's paradox by comparing marginal vs. adjusted region effects.

Pro tip: Use a mixed-effects model with random slopes for region if you expect region effects to vary over time, but be cautious about overfitting; also, always visualize the adjusted effects with confidence intervals to make the results actionable for stakeholders.

1. Define the model and estimand

Specify a logistic regression (or beta regression) with response rate as the outcome, region and job category as fixed effects, and time as a fixed effect (e.g., week or month). The estimand is the adjusted odds ratio or marginal effect of region on response rate, holding category mix and time constant.

2. Handle standard errors and clustering

Use cluster-robust standard errors at the region level (or job level if repeated measures) to account for correlation within regions. Consider bootstrap or permutation tests if the number of regions is small.

3. Adjust for multiple comparisons

Apply a multiple testing correction (e.g., Benjamini-Hochberg FDR) to control the false discovery rate across many region comparisons. Report adjusted p-values or confidence intervals.

4. Detect Simpson's paradox

Compare marginal region effects (unadjusted) with adjusted effects from the model. If the direction or magnitude changes substantially, investigate confounding by job category or time. Use stratification or visualization to confirm.

5. Communicate effect sizes

Report adjusted response rates per region with confidence intervals, and translate differences into practical terms (e.g., percentage point lift, number of additional responses per 100 invitations). Use plots like forest plots or caterpillar plots to show variation.

Key Points to Mention

Use of fixed effects for region, job category, and time to control for confounding.
Cluster-robust standard errors to account for within-region correlation.
Multiple comparison correction (e.g., Benjamini-Hochberg) when testing many regions.
Simpson's paradox detection by comparing marginal and adjusted effects.
Effect size reporting: adjusted rates, odds ratios, and practical significance.
Consideration of interaction between region and time to assess temporal stability.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.